Referring now to prior art FIG. 1, there is shown a quarter car model of a passively suspended vehicle. The portion of the sprung mass corresponding to one corner of the vehicle is represented by the mass, M.sub.s, and the unsprung mass of the combined tire and hub assembly wheel at one corner by the mass, M.sub.u. The suspension is modeled as a linear spring having a spring constant, K.sub.s, and a linear damper having a damping rate, C.sub.s. The tire is represented by a spring stiffness, K.sub.u. Since the damping in the tire is typically very small it may be neglected. It may be assumed that the tire acts as a point contact follower that is in contact with the road at all times.
The vehicle is assumed to travel at a constant forward velocity over a random road surface. Road measurements have shown that accept at very low frequencies, the road profile (vertical displacement of the road surface) can be reasonably well approximated by an integrated white nose input. Hence, the vertical velocity at the tire-road interface may be modeled as a white nose input.
In the above quarter car model, the principle areas of analytical interest are vibration isolation, suspension travel and road holding characteristics of the vehicle. In performing the analysis of these characteristics, the vehicle response variables that need to be examined are the deflection of the sprung mass from the unsprung mass, x.sub.1, the deflection of the unsprung mass from the road surface, x.sub.2, and the vertical acceleration of the sprung mass, d.sup.2 (x.sub.1 +x.sub.2)/dt.sup.2. The rms vertical acceleration of the sprung mass may be used as a measure of the vibration level.
In the passively suspended vehicle based on the model of FIG. 1, the only suspension parameters that can be changed are the stiffness of the spring, K.sub.s, and damping rate, C.sub.s, respectively. By replacing the spring and damper shown in prior art FIG. 1 with a totally active system, four suspension parameters may as a result be controlled. In addition to active control of the spring constant between the sprung and unsprung masses (affecting the natural frequency of the sprung mass) and the active control of the absolute velocity of the sprung mass (affecting the damping), active control of the tire deflection (affecting the wheel hop frequency) and the velocity of the unsprung mass which affects the damping of the wheel hop mode) may also be provided. In the active suspension the damping of the sprung and unsprung mass modes can be specified independently. In contrast thereto, changes to the damping in the passive suspension affects the damping of both modes simultaneously.
Referring now to FIG. 2, there are shown two acceleration response curves of the vertical acceleration of the sprung mass plotted as a function of the frequency of the white noise input vibrations. FIG. 2 is obtained from R. M. Chalasani, Ride Performance Potential of Active Suspension Systems, Part I, Simplified Analysis Based On A Quarter Car Model, Power Systems Research Department, General Motors Research Laboratories, pp. 187-204. In Chalasani, an analysis and comparison is made between the quarter car model of the passive suspension of FIG. 1 and the quarter car mode of an ideal active suspension. FIG. 2 is but one result of the analysis. The acceleration response curves of the sprung mass shown in FIG. 2 indicate that the principle difference in system response between the purely active and the purely passive configurations occurs typically in the frequency range of 4 to 25 rad/sec (0.7 to 4 Hz). These numerical values were obtained using values for sprung mass, unsprung mass, spring constants and damping typically associated with softly sprung, lightly damped "family-type" vehicles.
The lightly damped passive suspension exhibits resonances at the sprung and unsprung mass natural frequencies, .omega..sub.s and .omega..sub.u, respectively. The active suspension exhibits a well damp behavior near the sprung mass natural frequency, .omega..sub.s, and a lightly damp behavior, similar to the passive suspension at the unsprung natural frequency .omega..sub.u. Since the rms vertical acceleration of the sprung mass is the measure of vibration level, most of the improvement in vibration isolation occurs in the low frequency range below 25 rad/sec. (4 Hz). FIG. 3 qualitatively illustrates that this frequency may be represented by a crossover frequency, .omega..sub.c, between body motion and wheel motion compensation concerns in the suspension. Generally, the crossover frequency, .omega..sub.c, lies between the natural frequencies, .omega..sub.s, and .omega..sub.u, of the sprung and unsprung mass.
In U.S. patent application Ser. No. 07/238,925, filed Aug. 31, 1988, an assigned to the assignee of the present application, there is described a novel electromagnetic linear actuator and an exemplary use of the actuator in an electromagnetic strut assembly. As described therein, a corrective current is applied to the coil of the linear actuator, wherein the control current affects the entire frequency range. It has been found that the system as described in the abovereference application can achieve a 15% improvement over a purely passive suspension system for road input frequencies above 4 Hz assuming an unlimited bandwidth of the control system. For practical applications, as is found in the Chalasani paper, this improvement becomes negligible.